Low memory crash with 500,000 particles
This error occurs when you do not have enough RAM for your scene. This could be cause by the particles, but it also may be something else in your scene. Try a blank scene with a particle system of 500,000 and see if you get the same error. If you don't, you'll need to optimize the other objects in your scene. Either way, a RAM upgrade is generally a good idea when getting into intense 3D arts.

Also, are you rendering on GPU? If so, try switching to CPU. GPU rendering uses VRAM, whereas CPU uses your computer's RAM.